The viscoelastic behavior of bone is not yet well understood though it has been studied for more than 30 years. Systematic time-dependent mechanical studies have been limited to macroscopic samples and yield conflicting results, probably due to the heterogeneous micro- and ultra-structural composition of the tested macro-samples.
The best available models of long bone shaft either posit homogeneity, based on elastic properties that hypothesize non-existent structural symmetries (Rho, 2000), or non homogeneity, but discounting the lamellar distribution pattern (for a review see, Ascenzi M.-G. et al., 2000). These models do not provide local information for clinical use in orthopaedic and reconstructive surgery and in the design and placement of implants and prostheses because such models do not account for the mechanical properties of bone ultra- and micro- structure.
The currently used morphological classification of adult human bone dates back to Petersen (1930) and views bone as a four-order hierarchy, of decreasing scale. The structures corresponding to gross shape, distinguished as compact and cancellous bone, comprise the first order or macrostructure. The second order of compact bone, microstructure, includes osteons (also known as harvesian systems), their coaxial lamellar layers, and additional related structures, e.g. marrow. The third order, ultrastructure, consists mainly of collagen bundles and hydroxyapatite crystallites with some protein mucopolysaccharides. Molecular patterning between organic and inorganic phases comprises the fourth order.
Osteons
Osteons are the predominant component of bone microstructure (see e.g. Bloom and Fawcetts, 1986). Osteons are centrally provided with a vascular canal bounded by concentric layers of lamellae, each a few microns thick. Osteonic lamellae show molecular organization of a mostly collagen bundle organic framework embedded in ground substance (comprised of sugars, proteins and water) and hydroxyapatite crystallites of orientation analogous to the collagen bundles'. Osteons, a few centimeters long, are between 200 and 300 μm diameter.
Two osteon types have been named after the direction of their fiber bundle direction arrangements, known as “longitudinal” and “alternate”. Longitudinal osteons consist of lamellae appearing dark under a polarizing microscope. Alternate osteons consist of lamellae appearing alternatively dark and bright. Dark lamellae, called longitudinal, consist of collagen bundles with marked longitudinal spiral course (Gebhardt, 1907). Bright lamellae, called transverse, were originally hypothesized by Gebhardt to consist of bundles with marked transversal course only, but have subsequently been found (Frasca et al., 1977; Giraud-Guille, 1988; Ascenzi A. et al., 2001) to include oblique bundles as well. Much is yet unknown about the properties and roles of these osteon components. However, longitudinal lamellae are thinner, richer in collagen, and poorer in hydroxyapatite crystallites than transverse lamellae (e.g., Marotti, 1993). Longitudinal lamellae are also hypothesized to contain more ground substance (Ascenzi A. et al., 2001).
The relative percent of mucopolysaccharides within any given osteon must decrease for its calcification to increase (Pugliarello et al., 1970). In fact, the remaining mucopolysaccharides need to form a substrate on which the hydroxyapatite crystallites can deposit and continue accumulating (Herring, 1971). Whether the low amount (less than 1%) of mucopolysaccharides makes a mechanical difference has not yet been investigated. Based on the results of a report by Sasaki and Yoshikawa, (1993), the relative percentage of mucopolysaccharides in each osteon type would probably differ between initial and final stages of calcification. Further, Minns et al. (1973) indicates that removal of ground substance in several connective tissues may decrease time-dependent mechanical effects.
Mechanical Testing of Osteons
Osteons have been studied for some 40 years. Frasca et al. (1976) isolated whole osteons from surrounding bone at their natural boundaries, but the irregular shape of osteons so isolated prevents systematic mechanical study. More recently, Ascenzi A. et al. (1994) provided a technique to isolate osteon samples of regular, uniform shape, suitable for systematic testing.
Mechanical testing of osteon samples has been limited to quasi-static monotonic testing (see Ascenzi M.-G. et al., 2000). Osteon sample testing uniformly confirms the dependence of their mechanical behavior on calcification, as established by the method of Amprino and Engstrom (1952) and collagen bundle direction distribution. Quasi-static cyclic torsional testing is underway (Ascenzi M.-G., 2000). The incompleteness of osteon research is principally due to the challenges presented by their microdimensions. Indeed, osteon sample isolation and testing is lengthy and requires competent personnel, as well as the custom design and fabrication of high-precision apparatuses for sample loading and property recording.
Viscoelasticity
Material science regards viscoelasticity as a characteristic feature of polymer containing materials. Bone, like most biological materials, contains polymers. Viscoelastic properties depend on temperature and moisture content, which the work will hold constant at physiological level. In viscoelastic materials, some of the elastic energy generated by application of external forces is dissipated as heat. Such dissipated energy may contribute to the force driving the bone remodeling process (Levenston and Carter, 1998).
Studies of the mechanisms that generate bone viscoelasticity, that can shed light on the physico-chemical origin of Wolff's law and the properties of osteons, have not yet been conducted. However, osteon viscoelastic behavior could differ between longitudinal osteons and alternate osteons at the same degree of calcification (initial and final) and within each osteon type between initial and final stages of calcification. The only reported mechanical testing of whole osteons, isolated at their natural boundaries, is a preliminary non-systematic monotonic dynamic torsional loading (Frasca et al., 1981). It indicates structure and strain dependence of shear storage modulus in osteons of unspecified type and degree of calcification, and a linear viscous behavior up to strain values of 10−4. However, this model does not explain the behavior of the osteon structural components.
Thus, there is a need in the art for a hierarchical geometric material bone model built on a solid understanding of bone ultra- and micro-structural mechanical properties. Such a model could provide clinicians with a tool to fundamentally improve the precision of their interventions. There is a further need in the art for knowledge about osteon sample behavior under dynamic loading in terms of osteon structural components. For such knowledge, the viscoelastic behavior of osteons, and the influence of calcification and collagen bundles' direction distribution on the viscoelastic behavior of osteons, will need to be elucidated. Another important parameter, the relative percentage of collagen and mucopolysaccharides in terms of osteon and lamellar types, has not yet been investigated. The work described herein addresses these and other needs in the art.